A type system for well-founded recursion

Fix-Point Equations for Well-Founded Recursion in Type Theory

Well-Founded Recursion over Contextual Objects

We present a core programming language that supports writing well-founded structurally recursive functions using simultaneous pattern matching on contextual LF objects and contexts. The main technical tool is a coverage checking algorithm that also generates valid recursive calls. To establish consistency, we define a call-by-value small-step semantics and prove that every well-typed program te...

Well-founded recursion with copatterns and sized types

In this paper, we study strong normalization of a core language based on System Fω which supports programming with finite and infinite structures. Finite data such as finite lists and trees is defined via constructors and manipulated via pattern matching, while infinite data such as streams and infinite trees is defined by observations and synthesized via copattern matching. Taking a type-based...

Dependent Type Theory with Parameterized First-Order Data Types and Well-Founded Recursion

We present a variation of Martin-Löf’s logical framework with βιequality, extended with first-order parameterized algebraic data types and recursive pattern-matching definitions. Our contribution is a proof of normalization for the proposed system, from which we obtain decidable type-correctness. Our result holds under the assumption that the call relation of the recursive definitions is well-f...

Xsb: a System for Eeciently Computing Well-founded Semantics

The well-founded model provides a natural and robust semantics for logic programs with negative literals in rule bodies. We implemented the well-founded semantics in the SLG-WAM of XSB 19]. Performance results indicate that the overhead of delay and simpliica-tion to Prolog | or tabled | evaluations is minimal. To compute the well-founded semantics, the SLG-WAM adds to an eecient tabling engine...